Question: Simplify the following expression: $ z = \dfrac{-2y + 10}{-5y} + \dfrac{-9}{7} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-2y + 10}{-5y} \times \dfrac{7}{7} = \dfrac{-14y + 70}{-35y} $ Multiply the second expression by $\dfrac{-5y}{-5y}$ $ \dfrac{-9}{7} \times \dfrac{-5y}{-5y} = \dfrac{45y}{-35y} $ Therefore $ z = \dfrac{-14y + 70}{-35y} + \dfrac{45y}{-35y} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{-14y + 70 + 45y}{-35y} $ $z = \dfrac{31y + 70}{-35y}$ Simplify the expression by dividing the numerator and denominator by -1: $z = \dfrac{-31y - 70}{35y}$